Instrument for the survey and solution of plane triangles in field work



-Apr. 24, 1923.

W. S. MOSES INSTRUMENT FOR THE SURVEY AND SOLUTION OF PLANE TRIANGLES INFIELD WORK Filed Aug. 22, 1921 7 2 Sheets-Sheet 1 William 5.1505425 IINVENTOR' ATTORNEY 1,453,078 w. s. MOSES Fil ed Aug. 22' 1921 2Sheets-Sheet 2 INVENTOR wuuam 3. Moses Apr. 24, 1923.

INSTRUMENT FOR THE SURVEY AND SOLUTION PLANE TRIANGLES IN FIELD WORK.Qaa

ATTORNEY Fatented Apr. 24, E923.

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INSTRUMENT FOR THE SURVEY AND SOLUTION D1 BLAKE ERIANGL'ES IN FIELbwean.

Application filed August 22, 1521. Serial No. {St-94,200.

\ To all whom it may concern:

Be it known that I, FVILLEAM lviosns, a citizen of the United States,residing at Onamia, in the county of Mille Laos and State of Minnesota,have invented a new and useful Instrument for the Survey and Solution ofPlane Triangles in Field l/Vork, of which the following is aspecification.

This invention relates to a new and improved means for finding anumerical ratio triangle for the solution of trigonometric problemscomprehended by the art of surveying or for the survey and solution ofall plane triangles in field work.

An object of this invention is to provide an instrument for determiningthe numerical values of the angles and sides of a triangle through asimilar triangle whose angles are equal and its sides proportionate tosaid triangle, the construction of the numerical unit triangle beingdetermined by the positioning of certain elements of the instrument withrespect to the similar position of the lines and angles forming thetriangle which it is attempted to compute.

The invention will be best understood from a consideration of thefollowing detailed description taken in connection with the accompanyingdrawing 'lorming part of this specification, with the understanding,however, that the invention is not confined to any strict conformitywith the showing in the drawing, but may be changed and modified so longas such changes and modifications mark no material departure from thesalient features of the invention as expressed in the appended claims.

In the drawing Fig. 1 is a side elevation of the device.

Fig. 2 is a plan view of the same.

Fig. 3 is a transverse section taken along the line 3-3 of Fig. 2.

Fig. 4- is a transverse section taken along the line 4+4 of Fig. 2.

Figs. 5, 6 and 7 represent diagrammatic views of the various positionsof the pivoted arms of the instrument and the unit base line.

In the drawings, 1 designates a tripod for supporting the instrumentprovided with a table 2 having an upstanding boss 3 which is perforated.I Arotatable disk 4 hasa depending pin 5 inserted in the perforationinthe boss, the pin being engaged by one end of a set screw 6 ,to preventrotation or the pin. r

The rotatable disk 4113s anupstanding per orated' lug 'Twhich is engagedupon op- POSliBSldQS byperiorated ears 8 depending rrom a disk 9. A pin10 havinga threaded portion passes through the alined perforations'otthe ears 8 and the lug? and is provided with a wing nut 11 adaptedtobe screwed upon the threaded end of the pin to securely hold the disk9 in adjusted relation with the rotatable disk 4. Mounted centrallyuponthe disk 9 is a vp'in'12 secured in the bottom of a base-line bar lAn eye-sight 14 and an object sight 15 are 10- cated uponoppositeen'dsof the base bar.

The base-line bar 13 is provided with a central horizontal line 16placed upon one side of the bar which forms the base of a numerical unittriangle presently to be described and designated more particularlythroughout the specification as the radix. A leveling tube 17 is securedin a socket located in the base bar. The central portion of the tubewhich is designated by the numeral 18, is disposed in av'ertical linepassing through the center of the instrument and is adapted to determinethe horizontal level of the base-line bar 13 and likewise the radix 16.A handle 19, secured toone end of the bar 13 and at the sighting endor". the instrument, is adapted-to rotate or t-ilt the bar when the wingnut 11 is loosened, for positioning the instrument ina horizontal,oblique or vertical plane.

Firmly secured to a vertical side of the bar 13 are two protractors 20and 21. the centers of which fall upon the ends of the radix or base ofthe unit triangle. A graduated arm 22, designated at the secant arm, ispivotally mounted on the bar 13, at the center 20 otthe protractor 20and is secured to a right angle operating rod 23 and spaced from theprotractor 20 by means of a washer or shim 24.

A telescope 25 is mounted upon the secant arm 22 by means of the straps26 Another graduated arm 27, designated at the tangent arm, is pivotallymounted on the bar 13 at the center 28 of the protractor 21 and securedto a right angle operating arm 29 which is mounted in bearings in thebar 13. By reason of the washer 24:, the arm 27 may be freely oscillatedby the sides of the arm 22, and bar 13. Both operating arms 23 and 29are fitted tightly in their bearings in order to insure against readydisplacement of the secant and tangent arms after they have beenadjusted.

The inner edge 30 of the arm 27, designated as the tangent ratio line,is adapted to form with the edge 31 of the arm 22 and designated as thesecant ratio line, an angle B which is called the angle of limitation.

The lines 30 and 31, together with the base line 16, form a numericalratio triangle which is capable of being made equi-angular with anytriangle, the numerical values of the sides and angles of which it isdesired to compute, employing the base or radix 16 as a unit line andwhich is divided into ten equal parts. The arms 22 and 27 are similarlygraduated by means of the same scale, each tenth part being divided intotenths and hundredths, thus graduating a unit decimally into tenths,hundredths and thousandths.

iinother telescope 32 is secured by means of straps 33 to the base bar13, and it will be seen that when the secant arm 22 has its secant ratioline 31 in alinement with the base or radix, that the telescopes 25 and32 will be in the same horizontal plane, and furthermore that when thearm 22 is oscillated upwardly and away from the line 16, the telescope25 will be oscillated and form an angle with the telescope 32, while thearm 22 passing over the protractor 20 will determine the numerical valueof the angle between the telescopes 25 and 32, and likewise between theradix and the secant ratio line 31. This angle, represented by A, isdesignated as the secant angle in Figs. 1, 5 and 6. 'lVhen the arm 27 isoscillated above or beneath the radix 16, the tangent ratio line 30 willform, with the radix 16, an angle designated as the tangent angle andrepresented by C, the numerical value of which may be read upon theprotractor 21. The angle B formed by the intersection of the tangentratio line 31 and the secant ratio line 30, forms the angle oflimitation of the triangle and is determined by adding angles A and Cand subtracting the sum from 180, or 180(A+C):B.

The secant arm 22 is provided with the eye-sight 3a and the object sight35.

The telescope 32 is provided with the eye piece 36 while the telescope25 is provided with eye-piece 37.

The graduated semi-circular part of protractor 21 located above radixline 16 is adapted for reading angles less than 180, that are formed bythe radix and the tangent ratio line above the radix, while thegraduated semi-circular partof the protractor below the radix is adaptedfor reading angles formed by the tangent ratio line and the radix whentangent arm 27 is rotated few of them will suffice to demonstrate theyapplication of my device.

If the two angles and a side of a triangle be given, the other angle andthe other two sides may be readily determined in the following manner InFig. 5, let ABC be any triangle, the angles A and C and the side ACbeing given.

To find angle B and sides AB and BC by means of the ratio triangle ABCof Figs. 1 and 5 formed by base line 16, secant line 31 and tangent line30, in the following manner I Rotate 22 until the secant angle A equalsA of the triangle. Also rotate tangent arm 27 until the tangent angle Cequals angle C of Fig. 5.

The angle of limitation B of Fig. 1 is equal to the angle 1 of Fig. 5.Since two angles of a triangle are equal to two angles of anothertriangle, the third angles are equal respectively to each other.

In the unit or ratio triangle shown in Fig. 1, line 16 being a unit andalso proportional to the side AC will bear the following ratio to lines30 and 31, respectively, of Fig. 1. Therefore, we will have thefollowing formulas from the triangles ABC of Fig. 1 and 5.

=secant ratio line;

I ig,-= tangent ratio line.

Suppose, for instance, that the known side AC, Fig. 5, is equal to 100feet, and as the line 16 of the ratio triangle in Fig. 1 is a unit line,and the length of the line 31 between the point 20 and the intersectionof the line with the line 30 of the arm 22, designated as AB, is read as61; (that is 6-1- tenths of unit line 16), line AB of the similartriangle ABC would be equal to 65 feet. The length of the line BC onarm, 2'? between the point 28, and the point where the line 31 cuts theline 30 is read as 4.9, the

anemone line BC will be -49 'hundredths of the unit line 16,andtherefore theside BC ofthe triangle ABC would be equal to 49 feet.

Any triangle may be computed through the numerical ratiotriangle shownin Fig. 1, when certainpa-rtsof the triangle are given, as, when I Aside and two angles are given, and when Two sides and-the includedangle, or opposite angles are given.

Also when the three sides are given.

For surveying and the solution of triangles in field work, telescope 32is mounted on the base-line bar 13 having its line of sight parallelwith the radix or unit baseline 16.

The telescope 25 is'inounted on the secant arm 22, having its line'ofsight parallel with the sec-ant ratio'line 31., The sight line of eachtelescope being equally spaced respectively from the unit base line 16and the secant ratio line 31, thereby producing two triangles which havetwo of their respective sides in coincidence and the third sideparalleled. Therefore, their angles are equi-angular and theirhomologous sides proportional.

In sighting the angles formed by the telescopes, or by the sights 14 and15, and the sights 85 and 3 1, the angle formed by the intersection ofthe respective sight lines is called the angle of sight and this-angleis placed over the point or station popularly known as the sight stationand from which the survey is to be made. After the sight station hasbeen located, the first step is to measure a side and locate an anglebetween that side and some unknown side which is necessary in thesolution of tri angles in surveying.

It will be noted that the line of sight through the eye sight 1% and theobject sight 15 is so placed on the base line bar 18 that it will befound to beat one side of and parallel with the radix line 16 fordetermining the position of the radial line of sight. Likewise, thesights 34 and 35 are so positioned on the secant arm 22 that their lineof sight will also be to one side and parallel with the secant ratioline 31 for determin- F ing the position of the arm 22, or more par-"ticularly the secant ratio line 31 or secant angle A.

It may further be stated that the sights 14, 15 and '34:, 35 may be usedjointly with the telescopes, or independently thereof.

Referring to :Fig. 6 of the drawings, D designates the ordinarystaifused in surveying and which is accordingly graduated and supplied withthe vanes B and C, the base d of the stafi resting upon the ground.

The instrument is located at the sight station A, while the staff D islocated at a point distant from the sight station. The distance betweenthe staff D and the sight station A is a line ofthe triangle A, :B, C,which is required to be determined and which may be accomplished in thefollowing manner The instrument illustrated in Fig. 1 is located at thesight station A, and by means of the leveling instrument 17, thebase-line bar 13 is horizontally positioned, and by means of the sights141- and 15 and telescope 32, the horizontal line AC which is an extension of the line AC, is determined. The line AC cuts the staff D asindicated by the vane C. The secant arm 22 is then rotated by means ofthe arm 23 and by means of the telescopes and the sights 35, 34, theangle betweenthe secant ratio line 31 and the unit base line 16 isdetermined, so that an extension of the line 31 will pass through I thehighest point of the staff D which is located at B forming the line AB.

The line B C on the staff being known, and which is say 10 feet, it willbe easy to findthe length of the line AG by means of the formulas justgiven which are applicable to the ratio triangle ABC. Lines BC and B Care perpendicular to the horizon tal line AC, and therefore the tangentarm 27 .will be located perpendicularly to the unit base line 16. SinceB C is the sight tangent, BC the tangent ratio line, AC-

the unitbaseline and AC the line to be determined, the numerical valueof the line AC is found as follows Reading the dimensions from the ratiotriangle we have,

AC:1 BO:1/100.

In Fig. 1, let an and Ache the sight lines and BC the third side of theratio triangle.

Let A be the sight station. From the sight station A, sight the radixline 16 on the base line bar 13 tostation or angle C, the line ACpassing through C." Sight the secant line AB to angle B. The angle A isread from protractor 20.

Now measure angle C. Angle B which is the angle of limitation isdetermined by the position of lines AB and BC. This completes the ratiotriangle, making the ratio triangle and the triangle to be determinedequi-angular. The following solution is appropriate 2- The side A'C ismeasured, (Fig. T To find BC and AB' AC times tangent ratio BC AC timessecant ratiozA'B Therefore, if AC is known, BC may be readily found byreading the value of the tangent line BC of the ratio triangle or theinstrument and that number multiplied by the base AC will give thelength of the side BC. AB may be found in the same manner lVhat isclaimed is p 1. A surveying instrument comprislng, 1n combination, abase-line bar, graduated arms pivotally mounted at spaced fixed pointson the base-line bar, the dlstance between said points representing aunit base of a numerical triangle, the other two sides of the trianglebeing formed by the adjacent edges of the pivoted arms, means torrotating the pivoted arms, and telescopes one of which is collimatedwith the baseline bar and the other with a pivoted arm.

2. A surveying instrument comprising, in combination, a base-line bar,graduated arms pivotally mounted at spaced fixed points on the base-linebar, the distance between said points representmg a unit base of anumerical triangle, the other two sides of the triangle being formed bythe adj acent graduated edges of the pivoted arms, means for rotatingthe pivoted arms, and telescopes collimated with the base-line bar andwith one or" the pivoted arms, one of said telescopes adapted to bepositioned at an angle to the other telescope. r

3. A surveying instrument comprising, in combination, a base-line bar,graduated arms pivotally mounted at spaced fixed points on the base-linebar and normally rotatable in a vertical or oblique plane, the distancebetween said points representing a unit base of a triangle, the othertwo sides of the triangle being formed by the adjacent edges of thepivoted arms, means for rotating the pivoted arms, telescopes collimatedwith the base-line bar and with one of the pivoted arms, and sight meanslocated on one of the pivoted means and on the base-line bar, the sightmeans and a telescope forming equal angles with a line passing centrallyof the base-line bar at all positions of one of the arms.

4. A surveying instrument comprising, in combination, a base-line bar,graduated arms pivotally mounted at spaced fixed points on the base-linebar and normally rotatable in any plane, the distance between saidpoints representing a unit base of triangle, the other two sides of thetriangle being formed by the adjacent edges or the pivoted arms, meansfor rotating the pivoted arms, and sight means located on one of thepivoted means and on the base-line bar, the lines of sight through saidsight means being collimated with two sides of the triangle to determinethe sight angles of the triangle.

5. A surveying instrument comprising, in combination, a base-line bargraduated arms pivotally mounted at spaeed fixed points on the base-linebar and normally rotatable in avertical or other plane, the distancebetween the fixed points reprev senting a unit base of a triangle, theother two sides of the triangle being formed by the adjacent edges ofthe pivoted arms, telescopes collimated with the base-line bar and withone of the pivoted arms, and sight means located on one of the pivotedmeans and on the baseline bar, said telescopes and sight means beingrespectively located normally in the same horizontal planes.

6. A surveying instrument comprising, in combination, a base-line bargraduated arms pivotally mounted at spaced fixed points on the base-linebar and normally rotatable in a vertical plane, the distance betweensaid points representing a unit base of a triangle, the other two sidesof the triangle being formed by the adjacent edges ot the pivoted arms,means for rotating the pivoted arms, telescopes collimated with thebase-line bar and with one of the pivoted arms, sight means located onone of the pivoted means and on the base-linebar, the sight means beingin alinement with the pivotal points of the oscillating arms, and meansfor alining one edge oi a pivoted with line passing through the sightmeans and the pivotal points of the arms.

7. In a surveying instrument comprising base bar provided with a baseline, means for determining the horizontal position of the line,graduated arms pivotally mounted at spaced fixed points on the line, thedistance between said points representing the unit base of a triangle,the other two sides of the triangle being formed by the adjacent edgesof the pivoted arms and the length or the sides of the triangle beingdetermined by the intersection of said pivoted arms, one of said armsadapted to be positioned perpendicular to the base line, the other armforming an acute angle with the base line, and sighting means on thebase bar and arranged in a plane passing through the base line.

8. A surveying instrument comprising,

in combination, a base-line bar graduated arms pivotally mounted atspaced fixed points. on the base-line bar, the distance between saidpoints representing a unit base 01"" a numerical triangle, the other tWosides of the triangle being formed by the adjacent edges 01 the pivotedarms, means for rotating the pivoted arms, and telescopes one of whichis collimated with the base' line bar and the other with a pivoted arm,and means for adjustably supporting the instrument.

In testimony, that I claim the foregoing as my own, I have heretoaflixed my signature.

WILLIAM S. MOSES.

